Normalized solutions for Schrödinger systems in dimension two

In this paper, we study the existence of normalized solutions to the following nonlinear Schrödinger systems with exponential growth{−Δu+λ1u=Hu(u,v),in R2,−Δv+λ2v=Hv(u,v),in R2,∫R2|u|2dx=a2,∫R2|v|2dx=b2, where a,b>0 are prescribed, λ1,λ2∈R and the functions Hu,Hv are partial derivatives of a Cara...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-10, Vol.538 (1), p.128323, Article 128323
Main Authors: Deng, Shengbing, Yu, Junwei
Format: Article
Language:English
Subjects:
Critical exponential growth
Nonlinear Schrödinger systems
Normalized solution
Trudinger-Moser inequality
Variational methods
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Summary:In this paper, we study the existence of normalized solutions to the following nonlinear Schrödinger systems with exponential growth{−Δu+λ1u=Hu(u,v),in R2,−Δv+λ2v=Hv(u,v),in R2,∫R2|u|2dx=a2,∫R2|v|2dx=b2, where a,b>0 are prescribed, λ1,λ2∈R and the functions Hu,Hv are partial derivatives of a Carathéodory function H with Hu,Hv satisfying exponential growth in R2. Our main result is totally new for the Schrödinger system in R2. Using the Pohozaev manifold and variational methods, we establish the existence of normalized solutions to the above problem.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128323